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11.5 Similar Triangles. Identifying Corresponding Sides of Similar Triangles. By: Shaunta Gibson. Similar Triangles are triangles that have the same shape but not necessarily the same size. B. E. D. F. C. A.

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## 11.5 Similar Triangles

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**11.5 Similar Triangles**Identifying Corresponding Sides of Similar Triangles By: Shaunta Gibson**Similar Triangles are triangles that have the same shape but**not necessarily the same size. B E D F C A In the diagram above, triangle ABC is equal to triangle DEF. We write it as ABC ~ DEF. In the diagram, each angle of ABC corresponds to an angle of DEF as follows:**Similar Triangles are triangles that have the same shape but**not necessarily the same size. B E C F A D angle A = angle D angle B = angle E angle C = angle F Also, each side of ABC corresponds to a side of DEF AB corresponds to DE BC corresponds to EF AC corresponds to DF**In similar triangles, corresponding sides are the sides**opposite the equal angles. * When we write that two angles are similar, we name them so that the order of corresponding angles in both triangles is the same. triangle ABC ~ triangle DEF B E D F A C**Triangle RST ~ triangle XYZ. Name the corresponding sides of**these triangles. Because RST ~ XYZ that means angle R = angle X, angle S = angle Y, and angle T = angle Z. Now we write the following: Angle R = Angle X, so ST corresponds to YZ. Angle S = Angle Y, so RT corresponds to XZ. Angle T = Angle Z, so RS corresponds to XY. T Z S R X Y**In similar triangles, corresponding sides are in proportion:**that is, the ratios of their length are equal. As shown below in the example triangle ABC ~ DEF, therefore we have the following B AB BC AC DE EF DF 6 8 4 18 3 4 2 9 8 cm 6 cm A C 4 cm E 2 4 cm 3 cm 1 D F 2 cm**Finding the Missing Sides of Similar Triangles**• To find a missing side of similar triangles 1.) write the ratios of the lengths of the corresponding sides 2.)write a proportion using a ratio with known terms and a ratio with an unknown term 3.) solve the proportion for the unknown term**In the following diagram, triangle TAP ~ triangle RUN. Find**x. Because TAP ~ RUN, we write the ratios of the lengths of the corresponding sides. A N x 15 cm 12 cm 9 cm T P R 18 cm U 30 cm • 15 x x 30 12 18 or 9 12**Now cross multiply, then divide to get the length of AP.**A N x 15 cm 12 cm 9 cm T P R 18 cm U 30 cm • 15 x 9x = 180: x = 20 so x, or the length of AP, is 20 cm 9 12**THANK YOU**E T H E N D

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